Skip to main content
Back

Simplifying Rational Expressions quiz

Control buttons has been changed to "navigation" mode.
1/15
  • What is a rational expression?
    A rational expression is a quotient of two polynomials, similar to how a rational number is a quotient of two integers.
  • What must you always check in the denominator of a rational expression?
    You must check that the denominator is not zero, because division by zero makes the expression undefined.
  • How do you find the values for which a rational expression is undefined?
    Set the denominator equal to zero and solve for the variable; these values make the expression undefined.
  • What is the first step in simplifying a rational expression?
    The first step is to factor both the numerator and the denominator completely.
  • After factoring, what do you do to simplify a rational expression?
    Cancel any common factors that appear in both the numerator and the denominator.
  • What is the simplified form of (28x^3)/(35x^5)?
    The simplified form is 4/(5x^2).
  • If you have x plus two times x minus two over x plus six times x plus two, what is the simplified expression?
    The simplified expression is (x - 2)/(x + 6).
  • How do you factor 3x^2 - 15x?
    You factor out the greatest common factor, which is 3x, giving 3x(x - 5).
  • What is the result of simplifying (x - 5)/(3x^2 - 15x)?
    The result is 1/(3x).
  • What happens when you divide an expression by its opposite?
    Dividing an expression by its opposite gives -1, just like dividing a number by its opposite.
  • Are x + 3 and x - 3 opposite factors?
    No, x + 3 and x - 3 are conjugates, not opposites, because not all terms have opposite signs.
  • How can you check if two expressions are opposites?
    Factor out a -1 from one expression; if it becomes identical to the other, they are opposites.
  • What is the simplified result of (10 - x)/(x - 10)?
    The simplified result is -1.
  • What is the simplified form of (x + 3)(3 - x)/(x - 3)?
    The simplified form is -x - 3.
  • Why is it important to factor completely before simplifying a rational expression?
    Factoring completely ensures all common factors are visible and can be canceled, leading to the simplest form.